That might be a good solution. I am still having problems with it though.
1) Not really essential but: Why don't I simply get an "No module named 'sqlite3'" if sqlite3 is not included? Instead I get the error posted above.
2) When I first add the modules path from your local Python distribution to ST3 and then try to import 'sqlite3', I still get an error (see below). In my case the path is '/Library/Frameworks/Python.framework/Versions/3.3/lib/python3.3' (PATH variable below).
Traceback (most recent call last):
File "<string>", line 1, in <module>
File "/Library/Frameworks/Python.framework/Versions/3.3/lib/python3.3/sqlite3/__init__.py", line 23, in <module>
from sqlite3.dbapi2 import *
File "/Library/Frameworks/Python.framework/Versions/3.3/lib/python3.3/sqlite3/dbapi2.py", line 26, in <module>
from _sqlite3 import *
ImportError: No module named '_sqlite3'